DiscreteDists (version 1.0.0)

DGEII: The DGEII distribution

Description

The function DGEII() defines the Discrete generalized exponential distribution, Second type, a two parameter distribution, for a gamlss.family object to be used in GAMLSS fitting using the function gamlss().

Usage

DGEII(mu.link = "logit", sigma.link = "log")

Value

Returns a gamlss.family object which can be used to fit a DGEII distribution in the gamlss() function.

Arguments

mu.link

defines the mu.link, with "logit" link as the default for the mu parameter. Other links are "probit" and "cloglog"'(complementary log-log).

sigma.link

defines the sigma.link, with "log" link as the default for the sigma.

Author

Valentina Hurtado Sepúlveda,

Details

The DGEII distribution with parameters \(\mu\) and \(\sigma\) has a support 0, 1, 2, ... and mass function given by

\(f(x | \mu, \sigma) = (1-\mu^{x+1})^{\sigma}-(1-\mu^x)^{\sigma}\)

with \(0 < \mu < 1\) and \(\sigma > 0\). If \(\sigma=1\), the DGEII distribution reduces to the geometric distribution with success probability \(1-\mu\).

Note: in this implementation we changed the original parameters \(p\) to \(\mu\) and \(\alpha\) to \(\sigma\), we did it to implement this distribution within gamlss framework.

References

nekoukhou2013DiscreteDists

See Also

dDGEII.

Examples

# Example 1
# Generating some random values with
# known mu and sigma
set.seed(189)
y <- rDGEII(n=100, mu=0.75, sigma=0.5)

# Fitting the model
library(gamlss)
mod1 <- gamlss(y~1, family=DGEII,
               control=gamlss.control(n.cyc=500, trace=FALSE))

# Extracting the fitted values for mu and sigma
# using the inverse link function
inv_logit <- function(x) 1/(1 + exp(-x))

inv_logit(coef(mod1, what="mu"))
exp(coef(mod1, what="sigma"))

# Example 2
# Generating random values under some model

# A function to simulate a data set with Y ~ GGEO
gendat <- function(n) {
  x1 <- runif(n)
  x2 <- runif(n)
  mu    <- inv_logit(1.7 - 2.8*x1)
  sigma <- exp(0.73 + 1*x2)
  y <- rDGEII(n=n, mu=mu, sigma=sigma)
  data.frame(y=y, x1=x1, x2=x2)
}

set.seed(1234)
datos <- gendat(n=100)

mod2 <- gamlss(y~x1, sigma.fo=~x2, family=DGEII, data=datos,
               control=gamlss.control(n.cyc=500, trace=FALSE))

summary(mod2)

# Example 3
# Number of accidents to 647 women working on H. E. Shells
# for 5 weeks. Taken from
# Nekoukhou V, Alamatsaz MH, Bidram H (2013) page 886.

y <- rep(x=0:5, times=c(447, 132, 42, 21, 3, 2))

mod3 <- gamlss(y~1, family=DGEII,
               control=gamlss.control(n.cyc=500, trace=FALSE))

# Extracting the fitted values for mu and sigma
# using the inverse link function
inv_logit <- function(x) 1/(1 + exp(-x))
inv_logit(coef(mod3, what="mu"))
exp(coef(mod3, what="sigma"))